| Инд. авторы: | Vaskevich V.L., Shvab I.V. |
| Заглавие: | Quasilinear integrodifferential Bernoulli-type equations |
| Библ. ссылка: | Vaskevich V.L., Shvab I.V. Quasilinear integrodifferential Bernoulli-type equations // Journal of Physics: Conference Series. - 2019. - Vol.1391. - Art.012075. - ISSN 1742-6588. - EISSN 1742-6596. |
| Внешние системы: | DOI: 10.1088/1742-6596/1391/1/012075; РИНЦ: 43241656; SCOPUS: 2-s2.0-85077817614; WoS: 000554820300075; |
| Реферат: | eng: The equations considered in this article have the form in which the time derivative of the unknown function is expressed as a double integral over the space variables of a weighted quadratic expression of the sought function. The domain of integration is unbounded and does not depend on time but depends on the space variable. We study the Cauchy problem in the function classes accompanying the equation with initial data on the positive half-line. In application to this problem, the convergence of the successive approximation method is justified. An estimate is given of the quality of the approximation depending on the number of the iterated solution. It is proved that, on some finite time interval, the posed Cauchy problem has at most one solution in the accompanying function class. An existence theorem is proved in the same class. © 2019 IOP Publishing Ltd. |
| Ключевые слова: | Time derivative; Successive approximation methods; Function class; Finite time intervals; Existence theorem; Double integrals; Domain of integration; Cauchy problems; Approximation theory; Integrodifferential equations; |
| Издано: | 2019 |
| Физ. характеристика: | 012075 |
| Конференция: | Название: 8th International Conference on Mathematical Modeling in Physical Science Город: Bratislava Страна: Slovakia Даты проведения: 2019-08-26 - 2019-08-29 |